The purpose of this
lab exercise is to model the effects of natural selection on the appearance and
genetic make-up of a natural population (the peppered moth). We will construct
a STELLA model for this population that incorporates the basic principles of
population genetics.

Figure 1

The peppered moth (Bistonbetularia)

Before we begin, we
will need to define some important genetic terminology:

Alternative forms of a gene
are called alleles; All sexually reproducing organisms have two alleles - one inherited from each parent

The genetic constitution of
an individual is called its genotype

The physical expression of a
genotype is called the phenotype

If two alleles are identical,
an individual is said to be homozygous for that gene; if two
alleles are different, the individual is said to be heterozygous

A dominant allele has
such a strong phenotypic effect in heterozygous individuals that it
conceals the presence of the weaker (recessive) allele

Introduction

The case of the peppered
moth (Bistonbetularia) is a classic example of
evolution through directional selection (selection favoring extreme
phenotypes). Prior to the industrial revolution in England (pre-1740), the peppered
moth was found almost entirely in its light form (light body colored with black
spots). The moths would spend daylight hours on trees covered by light colored
lichen, their light colors giving them almost perfect camouflage against
predatory birds. There were a few dark individuals in the population, but their
occurrence was very rare. Scientists have determined that body color in the
peppered moth is controlled by a single gene.

The allele (version
of the gene) for dark body color is dominant, which means that a moth
possessing at least one such allele will have a dark body. To have a light
body, the moth has to have both alleles for light body color.

Dark moths were at a
distinct disadvantage, however, due to their increased vulnerability to bird
predation. Thus the frequency of the dark allele was very low (about .001%),
maintained primarily by spontaneous mutations from light to dark alleles. By
1819, the proportion of dark moths in the population had increased significantly.
Researchers found that the light-colored lichens covering the trees were being
killed by sulfur dioxide emissions from the new coal burning mills and
factories built during the industrial revolution. Without the light background
of the trees, the light moths were more visible to vision-oriented predators
(birds). They were losing their selective advantage to the dark moths, which,
against the treesí dark bark background, were less visible to birds. In 1848,
the dark moths comprised 1% of the population and by 1959 they represented ~90%
of the population. So, in 100 years the frequency of dark moths increased by
1000 fold!

Figure 3

Composition of various populations
of the peppered moth in the British Isles

In this exercise, we
will construct a model simulating the effects of differential predation
pressures on a hypothetical peppered moth population. To do this, we will need
to incorporate the genetics of moth body color into a population dynamics
model. We are assuming that body color is the only trait that confers any
significant selective advantages on peppered moths.

Building the Model

As you build this model, you will have to use ghosts to create copies for
duplicate variables. However, it is extremely important to make the
"Total Moths" converter in the lower part of the model the original.
Make sure the ghost stocks are in the lower part of the model. Then, all the
other ones can be ghosts copied off of it.

Ultimately, the structure of your model will look like this:

Figure 4

STELLA model of the peppered moth

As with any system,
we must first identify and define the stocks and flows of the system.

Stocks

Start to build your model by creating the following three stocks. We have three
different genotypes represented in our model:

AA mothies:
homozygous
dominant moths that are dark in color

Aamothlets:
heterozygous
moths that are also dark in color

aa moths: homozygous recessive moths
that are light in color

Note: STELLA will
not let you repeat variable names. Because STELLA is not case sensitive, it
doesnít distinguish between the names "aa
moths" and "Aa moths," so make sure to
vary them (i.e. "moths" vs. "mothlets.")

Flows

The flows of our
genotypic subpopulations are birth and death. First, take a look at the birth flows: Components on the right side of the equation are given below, and these will be your converters. First create the flows, then create the converters necessary for entering the equations into the flows, and then connect these converters to the flows with connectors. Finally, input the correct equations. At this point, you will not have entered any values for your converters, that will happen below.

The term for total
moths is calculated by using the ghost to make
copies of the 3 stocks and adding them together:

total moths = AA mothies + Aamothlets + aa moths

Also define
variables that calculate the relative frequencies of dark moths (AA and Aa) and light moths (aa):

dark freq = (AA mothies + Aamothlets) / total moths

light freq = aa moths / total moths

Now look at the
death flows for the stocks:

death1 = AA mothies * (natural mortality + bird predation dark)

death2 = Aamothlets * (natural mortality + bird predation
dark)

death3 = aa
moths * (natural mortality + bird predation light)

The death flows
incorporate a natural mortality rate as well as death resulting from predation
by birds. Notice that the bird predation rates are different for dark and light
moths. These two different predation rates are defined by:

bird predation light =
pollution * bird pred rate

bird predation dark = bird pred rate - ( pollution * bird pred
rate )

Bird predation rate
and pollution are both proportions between 0 and 1. Notice that with high rates
of pollution, bird predation light is higher, while bird predation dark is
highest when pollution is low.

Below are the
constants and rates that we have chosen for this model:

repro rate = .055

natural mortality = .045

bird pred
rate = .04

pollution = 0.0 (for now)

AA mothies
= 250

Aamothlets
= 500

aa moths = 250

Set up two graphs
for viewing results. The first (graph 1) should display dark freq and light
freq (this is the phenotype graph). Set up the second graph (graph 2) to display numbers of AA mothies, Aamothlets, and aa moths (this is the genotype graph). The
run specs for these runs are starting at 0.0 to 200.0 with a DT = 1.0, and the
time units set for years. Next, set up numeric displays (the blue button next to the graph) to
observe the numeric changes in allele frequencies (little a
allele and big A allele.) Donít forget to select "retain ending
value."

Investigating the System

Since pollution is
the true driver of the change in genotype frequency in the peppered moth
population, it is the variable that we are most interested in modifying.
Pollution is a proportional term, i.e. if it is zero there is no pollution and
when it equals 1, pollution is at a maximum.

Simulate the
following three scenarios with your model. For each scenario, savegraphs
1 (phenotypic response) and 2 (genotypic response) and copy and paste them into
your word document. Make sure to label each graph with the value of the
pollution variable (or write it in a caption under the graph).

Finally, run the model with a
changing pollution rate, which we can define graphically (as opposed to
mathematically). Click on and open the pollution converter, and then
select and click on the TIME function in the Built-ins list. (First delete
the value in the equation box.) Now click on the graphical function tab, and then the Graphical Function checkbox at the top of the panel. Notice that the X axis is TIME and the Y
axis is pollution.

Change the number at the top of
the Y-axis to 1.0 to restrict the range of pollution to between 0 and 1. Make
sure the X-axis ranges from 0 to 200, representing a time span of 200 years.
Next, using your mouse (or typing in the desired output), draw an s-shaped
graph that starts off at 0 (no pollution) and increases rapidly, then levels
off at 1 (maximum pollution) halfway across the graph (i.e. TIME ~100).

Figure 5

Screen Shot

Run the model under this pollution
scenario, copy and paste the graphs that reflect a rise in pollution near year
100 [graphs #5&6].

Now vary the timing of the rise in
pollution by shifting the position of the rise on the X-axis. Make two new graphs and note how the
timing affects the dynamics of the different genotypes[graphs #7&8].

Questions

Question 1

Turn in the graphs showing
phenotypic (graph 1) and genotypic (graph 2) responses in the moth population
for each of the scenarios that you've tested. [You should have eight graphs total at this point].

In a paragraph, describe the
dynamics you observe in each scenario. What happens to the genotypes and phenotypes of the moths when pollution is
added to the system (scenario 3)? Why?

Question 2

Name and describe the effects of
two significant assumptions we have made in the construction of this
model. What would be the effect of relaxing (changing) these assumptions?

Question 3

What would you expect to happen
(in terms of genotypic and phenotypic frequencies) if pollution levels
fluctuated widely? Check out your hypothesis by varying the pollution function
(add some spikes and dips to make it highly variable), include your graphs [graphs #9&10].

Question 4

What aspects of the model would
you change if the genotype "Aa" made the
moths gray (i.e. in between dark and light)? Adapt the structure of your model to reflect this change and include a screen shot. Note: We are not asking for you to enter equations or actually run the model - we only want you to change the structure of the model.

Question 5

If you changed the pollution levels in your new model with dark, light, and gray moths, predict how the new gray phenotype would fare? In your model, "life adapts to pollution levels and survives." Do you think this is representative of most real world situations? Explain.

As usual submit your one Word document as an attachment on Ctools, it should contain:

Answers to questions 1-5, with associated graphs (you should have 10 total graphs for the entire assignment). PLEASE make sure to label all your graphs!

Screenshot of your final model structure

Copy and paste final equations of your final model (at bottom of your Word document)